Rules for space when using mathrm{}

Question

I am using auto-generated Latex code from CAS system.  It uses mathrm{ln} and {mathrm e}.
The problem is the spacing between this and the letter before it, compared to when no mathrm is used.  The space is lost in the case with mathrm{ln}
Here is an example
documentclass[12pt]{book}
usepackage{amsmath}
usepackage{mleftright}  
mleftright

begin{document}
[
4 {mathrm e}^{3 x}+3 mathrm{ln}left(x right)
]
                      
[
4 e^{3 x}+3 lnleft(x right)
]                                                                                                              
end{document}

Compiled with lualatex, gives

I prefer the second one. The space before mathrm e has not changed. But the space before mathrm{ln} was lost.
Why is that? Is it then not approrpiate to use mathrm for ln?
TL 2020

egreg · Accepted Answer

Your autogenerated code is bad, sorry. In
3mathrm{ln}left(xright)

there are three atoms, namely

3 of type Ord
mathrm{ln} of type Ord
left(xright) of type Inner

Between two atoms of type Ord, TeX inserts no space.
To the contrary,
    3lnleft(xright)

contains again three atoms, but with a big difference, namely

3 of type Ord
ln of type Op
left(xright) of type Inner

TeX inserts a thin space (of the amount of thinmuskip) between an Ord atom and an Op atom.
Sorry, but “garbage in, garbage out”. If the software is able to recognize the string ln to be set in upright type, it could well take the initiative of outputting ln instead of the wrong mathrm{ln}.
By the way, also left and right are out of place. And it's quite interesting that “e” is translated into {mathrm e} instead of the more correct mathrm{e} (if you really insist into printing the Euler constant upright).
A fix.
documentclass[12pt]{book}
%usepackage{xparse} % not needed for LaTeX 2020-10-01 or later
usepackage{amsmath}
usepackage{mleftright}

mleftright

ExplSyntaxOn
NewCommandCopy{latexmathrm}{mathrm}

RenewDocumentCommand{mathrm}{m}
 {
  str_case:nnF { #1 }
   {
    {e}{e}
    {i}{i}
    {ln}{ln}
    {log}{log}
    {sin}{sin}
    % ... add to the list
   }
   { latexmathrm{#1} }
 }
ExplSyntaxOff

begin{document}
[
4 {mathrm e}^{3 x}+3 mathrm{ln}left(x right)
]
                      
[
4 e^{3 x}+3 lnleft(x right)
]                                                                                                              
end{document}

For LuaLaTeX and unicode-math, the workaround has to be different.
documentclass[12pt]{book}
%usepackage{xparse} % not needed for LaTeX 2020-10-01 or later
usepackage{amsmath}
usepackage{mleftright}  
usepackage[mathit=sym,bold-style=ISO]{unicode-math}
setmathfont{Asana Math}[Scale=MatchLowercase]
setmainfont{Baskervaldx}[
  UprightFont=*-Reg,
  ItalicFont=*-Ita,
  BoldFont=*-Bol,
  BoldItalicFont=*-BolIta,
]

mleftright

ExplSyntaxOn
AtBeginDocument
 {
  NewCommandCopy{latexmathrm}{mathtextrm}
  RenewDocumentCommand{mathtextrm}{m}
   {
    str_case:nnF { #1 }
     {
      {e}{e}
      {ln}{ln}
      {log}{log}
      {sin}{sin}
      % ... add to the list
     }
     { latexmathrm{#1} }
   }
 }% end of AtBeginDocument
ExplSyntaxOff

begin{document}
[
4 {mathrm e}^{3 x}+3 mathrm{ln}left(x right)
]
                      
[
4 e^{3 x}+3 lnleft(x right)
]                                                                                                              
end{document}

Note that Baskervaldx.sty is not the right choice when fontspec is used.

Davislor · Answer

In this case, ln is what’s called a log-like operator.
You can use either ln, operatorname{ln} or mathop{mathrm{ln}} to get spacing like log.  You can also add nolimits if you don’t like how subscripts and superscripts get placed above and below in display mode.
If amsmath did not already define it, you could write providecommandln{operatorname{ln}} and then have a ln command you could use in your source, and be able to tweak in one easy-to-find place.

Rules for space when using mathrm{}

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